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 March 14th, 2009, 08:42 PM #1 Member   Joined: Feb 2009 Posts: 76 Thanks: 0 level surfaces of function How do you describe the level surface of this function f(x,y,z) = x^(2) + 3y^(2)+ 5z^(2) This seems like a family of ellipsoids but I really dont know for sure.
 March 14th, 2009, 11:50 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: level surfaces of function That's correct. Rearranging, it looks like this: $\frac{x^2}{1^2}+\frac{y^2}{(1/\sqrt{3})^2}+\frac{z^2}{(1/\sqrt{5})^2}= c$ When c is positive, this level surface is an ellipsoid.

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### how do i find out what the level surfaces of x^2 3y^2 5z^2 is

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